I've been doing some amateur simulations of particle trajectories in a few well-known metrics (using GNU Octave and Maxima), and in the case of the Schwarzschild and Gullstrand-Painleve metrics I have the ability to check my results using freely available equations for conservation of energy and angular momentum. In the case of the Doran metric however, the geodesic equations are far messier(!), but I believe I now have a "correct" simulation. I would like to check this also, but have not seen any reference to equations for conserved quantities for this metric. Has anyone here looked into this, or does anyone know any useful links, or are there any computer algebra wizards that can help?